Exact electromagnetic duality with nonminimal couplings.

We study dyonic black hole solutions in the simplest nonminimal extension of Einstein-Maxwell theory that preserves electromagnetic duality. Any such theory involves an infinite tower of higher-derivative terms whose computation and summation usually represents an inaccessible problem. However, we show that upon assumption of a static and spherically symmetric ansatz, the whole series of higher-curvature terms can be summed up, giving rise to a fully nonlinear reduced action whose equations of motion are invariant under rotations of the electric and magnetic charges. From this result we compute the perturbative corrections to the Reissner-Nordstr\"om solution, and in the case of extremal black holes we determine exactly the near-horizon geometry as well as the entropy. Remarkably, the entropy only possesses a constant correction despite the action containing an infinite number of terms. In addition, we find there is a lower bound for the charge and the mass of extremal black holes. When the sign of the coupling is such that the weak gravity conjecture is satisfied, the area and the entropy of extremal black holes vanish at the minimal charge.